Some carburetors for gasoline fueled small engines such as two-stroke engines for handheld power tools such as chain saws, weed trimmers, leaf blowers and the like have carburetors with an internal accelerator pump which supplies additional fuel to the operating engine as the throttle valve of the carburetor is opened from its essentially closed or idle position toward its completely wide open throttle position. This additional fuel is needed to smoothly and rapidly accelerate the engine without stumbling particularly when it is under a load. Many prior accelerator devices have a positive displacement pump with a piston actuated by rotation of a shaft of a throttle valve through a wide variety of mechanical cam and linkage arrangements. One problem with these positive displacement accelerator pumps is they supply an excess quantity of fuel producing an overly rich fuel mixture for the engine upon initial opening of the throttle from its idle position and particularly if the throttle is opened or advanced to only an intermediate position which is less than the wide open throttle position. This is particularly a problem with a handheld power tool because many operators tend to rather rapidly partially open and close the throttle several times before fully opening and maintaining the throttle at its wide open position for a period of time during which a power tool is in actual use and its engine is under a substantial load.